J. Cent. South Univ. Technol. (2011) 18: 479-489

DOI: 10.1007/s11771-011-0721-7

Adaptive resource allocation for multi-user multi-server power-line communication OFDM systems

XU Zhi-qiang(徐志强)¹, ZHAI Ming-yue(翟明岳)², CUI Xiang(崔翔)², ZHAO Yu-ming(赵宇明)³

1. Hunan Electric Power Test and Research Institute, Changsha 410007, China;

2. Department of Electric and Electron Engineering, North China Electric Power University, Beijing 102206, China;

3. Technology Research Center of China Southern Power Grid, Guangzhou 510000, China

? Central South University Press and Springer-Verlag Berlin Heidelberg 2011

Abstract: The bits and power allocation model of adaptive power-rate mixture for multi-user multi-server power-line communication systems was analyzed with the restrictions of maximal total power, fixed rate for each real time (RT) user, minimal rate for each non-real time (NRT) user, maximal bits and power for each subcarrier in each orthogonal frequency division multiplexing (OFDM) symbol. An algorithm of resource dynamic allocation in the first OFDM symbol of each frame and resource optimal adjustment in the latter OFDM symbol of each frame was proposed. In the first OFDM symbol of every frame, resource is firstly assigned for RT users so as to minimize their total used power until satisfying their fixed rates; secondly the remainder resource of power and subcarriers are assigned for NRT users so as to minimize their total used power until satisfying their minimal rates also; lastly the remainder resource is again assigned for NRT users according to the proportional fairness strategy so as to maximize their total assigning rate. In the latter OFDM symbol of each frame, bits are swapped and power is adjusted for every user based on the resource allocation results of anterior OFDM symbol. The algorithm is tested in the typical power-line channel scenarios and the simulation results indicate that the proposed algorithm has better performances than the classical multi-user resource allocation algorithms and it realizes the multiple aims of multi-user multi-server resource allocation for power-line communication systems.

Key words: power-line communications; adaptive orthogonal frequency division multiplexing; resource allocation; user priority; swap adjustment

1 Introduction

The orthogonal frequency division multiplexing (OFDM) has become the major technology for realizing the high-speed data transmission of power-line communication (PLC) systems. But, it will be difficult to ensure the quality of service (QoS) of the system if only the traditional OFDM technology is used, due to the characteristics of time-varying and frequency-selecting, the large noise and interference power, and the serious signal attenuation and multiple restrictions for power-line channel [1]. Adaptive OFDM can dynamically allocate subcarriers to each user and the number of bits with relevant transmitting power to each subcarrier based on the channel states of each user, and effectively improve the effect of frequency-, time- and space-selective fading channel for the high-speed communications of PLC system [2]. So, the rational utilization of adaptive OFDM and optimal resource allocation technology can maximize the total assigning rate or minimize the total power used, and effectively improve the resource efficiency and service quality of the system.

The key issue of resource optimization allocation in the multi-user adaptive OFDM systems is the optimal allocation of subcarrier, bit and power. Currently, many dynamic multi-user resource allocation algorithms were proposed for different optimal objectives and restrictive conditions. In Ref.[3], a joint optimal allocation algorithm was proposed to maximize the throughput of the wireless multi-user OFDM system and the simulation results show that its performances are close to those of the simulated annealing algorithm but its complexity is lowered greatly. In Ref.[4], a multi-user and multi-carrier bit allocation algorithm was proposed for the high-speed DSL communication systems to minimize the total transmitting power while meeting all the required rates of the users. In Ref.[5], a simple subcarrier and bit allocation algorithm was given according to the priority of user, and the simulating performances were also given. In Ref.[6], an adaptive resource allocation algorithm for downlink OFDM/SDMA systems was proposed to maximize the throughput of the system by ensuring the QoS requirements of different users. Although many resource allocation algorithms are used to assign every subcarrier to the user with good channel state so as to improve the frequency efficiency of the system by fully utilizing the diversities of frequency-selection and multi-user, it could not ensure the fairness between the users and the QoS of each user, thus the max-min strategy and the proportional fairness strategy were proposed. In Ref.[7], a rate-maximum or power- minimum problem was considered for the transmitting rates of the user satisfying the max-min strategy, but the strategy could not satisfy the needs of multi-user and multi-service, and it made the resource efficiency of the system very low by assigning less resource to the good channel and more resource to the bad channel. In Ref.[2], a suboptimal resource allocation based on the proportional fairness strategy was realized for the multi-user’s QoS, which in the resource allocation model appended a condition that the rates incarnating the different server requirements among the users were taken as the way of nonlinear proportional restriction values and the restriction values were ascertained. Otherwise, this strategy could have the scenarios that the assigned resource of all users is not dissatisfied with the resource insufficience of the system or the resource utilization is deficient with the sufficient resource of the system. Since getting the system fairness is generally at the cost of losing system performances, the different fairness strategies among the users are the tradeoffs between the fairness and performance of the system. In Ref.[8], the maximal utility function strategy based on different bargaining floors was proposed so as to realize different tradeoff degrees of resource utilization of the system and different service fairness in different conditions, which is the stretch of the max-min strategy and proportional fairness strategy essentially. In Ref.[9], the transmission of real time (RT) or non-real time (NRT) service is a capacity problem that the required rate must be completed in the limited periods without reference to the diversification of the channel, so that the fairness of the system was realized by satisfying the required rate of every user in the duration of resource allocation.

Although there were many studies on the multi-user resource allocation, they were not aimed at the PLC systems. In Ref.[2], a subcarrier and power allocation algorithm with the limitation of power spectrum density (PSD) was proposed for the indoor OFDM-based PLC systems, and the performances of algorithm were simulated in many variable channel conditions. In Ref.[10], a bit allocation algorithm with the restriction of PSD was designed for PLC systems based on the greedy principle and the optimal allocation rule to reduce the computational complexity. On the basis of Ref.[10], a swapping algorithm with actual restrictions of high-speed PLC was discussed in Ref.[11] according to the different optimization criteria.

Although the works above have researched the multi-user resource allocation problems in PLC systems, these studies did not take the QoS requirements of multi-service and the priorities of multi-user into account. Moreover, in these studies, the possible minimum of total power used and then the possible maximum of total assigning rate under the remainder power of the system were not considered after satisfying the required rates for all users with the power and rate restrictions. Although there have been some studies on the fair resource allocation between QoS of the multi-user, the characteristics of services of the multi-user and whether the scenarios of the resource of the system are sufficient or scarce are not thought over.

In this work, a bit and power allocation model with rate and power adaptation for multi-user multi-service OFDM-based PLC system is analyzed with the various restrictions. Then, an algorithm of resource dynamic allocation in the first OFDM symbol of each frame in the system and resource optimal adjustment in the latter OFDM symbol of each frame in the system is proposed, which is simulated in some typical power-line channel environments.

2 Resource allocation model

Suppose that there are N subcarriers in each OFDM symbol for the OFDM-based PLC systems, which serve two kinds of users with the total user set of Ω and the user number of K₁+K₂. The K₁ users compose the RT user set Ω₁ with the fixed rate R_k1 bit/symbol and the target BER P_e1 for every RT user k, and the K₂ users compose the NRT user set Ω₂ with the fixed rate R_k2 bit/symbol and the target BER P_e2 for every NRT user k. Since every subcarrier could only be used by one user, there is not interference between users. The assigned bits r_k,n at each subcarrier n for user k can be expressed as

                       (1)

where p_k,n and g_k,n are the assigned power and the unit power signal-to-noise ratio (SNR) of the channel for user k on sub-carrier n, respectively, [x] is a operation rule that gets a maximal integer no larger than x. Γ_k is the SNR gap of user k depending on the target BER, the applied coding and the system margin which reflects the immunity about the SNR degradation. If un-coded M-ary quadrature amplitude modulation is employed with the same BER for user k on each subcarrier, Γ_k is approximately written by

                    (2)

where Q^-1(x) is the inverse error probability function. The power needed for user k on subcarrier n is written as

                                     (3)

In order to satisfy the electromagnetic compatibility of PLC systems, the total transmitted power P_t in each OFDM symbol and the signal power upper limit  on each sub-carrier n could be ascertained by adopting cognitive radio technology [12]. For the simplification of system realization, the assigned number of bits, r_k,n, is a non-negative integer no larger than b. For the practical PLC systems with the aforementioned restrictions in each OFDM symbol, the total power used firstly decreases possibly with ensuring the fixed rates of all RT users, and then it also decreases possibly with satisfying the minimal rates of all NRT users, and lastly the remainder resource of the system is assigned for all NRT users according to the proportional fairness strategy so as to increase the total rate of the system possibly.

The practical model of resource optimal allocation problem can be formulated by

     (4)

where a[0, 1], is the utility factor of objective function. R_k is the assigned total rate for user, kΩ₂. c_k,n is a 0-1 integer variable that c_k,n=1 when subcarrier n is assigned to user k; while c_k,n=0, otherwise.

The resource allocation problem above is a mixed- integer nonlinear programming problem [13], which is solved by the usual optimization algorithm, such as the Gomory fraction cutting plane method and branch-bound method. Since there are 2(K₁+K₂)N discrete integer variables in Eq.(4) and the number of subcarrier N for the actual high-speed PLC systems is large, the complexity of usual algorithm is very large if solving the problem immediately. In order to reduce the complexity, many algorithms are proposed, such as the multilevel iterative water-filling algorithm [14] and Lagrangian relaxation algorithm [15]. Since the objective function of resource optimization is not convex and the constraint functions are nonlinear, the solution of iterative water-filling algorithm does not always get the globally optimal solution [16]. So, Lagrange relaxation algorithm can be used to solve the problem in Eq.(4), which could decompose the problem in Eq.(4) into the two sequent sub-problems according to the Lagrange decomposition theory. Then, the first executing resource allocation sub-problem can be written as

               (5a)

And the second executing remainder resource allocation sub-problem can be written as

       (5b)

For Eq.(5a), the Lagrange function can be formulated by

                                                      (6)

where λ_k and μ≥0, are the Lagrangian multipliers. According to Lagrangian relaxation dual decomposition theory, the former section of Eq.(6) could be disassembled into N following optimization sub- problems as [17]

           (7)

After gaining the optimal solutions of all sub- problems, Eq.(6) is convex about Lagrangian multipliers λ and μ, which has zero duality gap and satisfies the Karush-Knun-Tucker (KKT) conditions [9]. So, the optimal solution of Eq.(5a) can be attained by

                          (8)

For Eq.(5b), the Lagrange function can also be written as

                      (9)

where β_k≥0 and θ≥0, are Lagrange multipliers. Similarly, the former section of Eq.(9) can also be decomposed into N following the optimal sub-problems as

       (10)

After gaining the optimal solutions of all sub- problems, Eq.(9) is also convex about the multipliers β and θ, which has zero duality gap and satisfies the KKT conditions [9]. So, the optimal solution of Eq.(5b) can also be written as

                        (11)

However, during attaining the optimal solutions of Eqs.(8) and (11), the algorithm needs seeking for the Lagrangian multipliers iteratively and its complexity depends on the performance of seeking for multiplier directly. The existing search methods, i.e. dichotomy [18] or subgradient [19], have the insufferable complexity. Especially, when the user number K is larger than two, the convergent speed becomes very slow. According to Eq.(5), the optimization objectives could be realized by executing the same Lagrangian relaxation algorithm two times. So, a new resource optimization allocation algorithm is needed to reduce its complexity and improve its performances.

3 Resource allocation algorithm

Suppose that the resource of every frame of PLC systems could be disparted into the same M resources of OFDM symbols. The channel states of all users in each OFDM symbol are changeless, while they are alterable but not too large between different OFDM symbols of each frame, so the subcarrier allocation for all users can be considered to be invariable in each frame. Thus, in the first OFDM symbol of each frame, subcarriers are firstly allocated to users, then the bits and power are allocated to every subcarrier. The resource allocation of latter OFDM symbol in each frame only needs to swap bits and adjust power for every user on the basis of the resource allocation results of its anterior OFDM symbol. According to the optimal objectives of resource allocation and the situations of multi-user multi-service in Eq.(4) or Eq.(5), the resource of the first OFDM symbol is firstly assigned to RT users to minimize their total power used with meeting their fixed rates, then the remainder power and unused subcarriers are assigned to NRT users until the minimal rates of all NRT users are satisfied or the resource of the system is used up. If the  minimal rates of NRT users are all satisfied and the resource of the system is not used up, the remainder resource of the system is assigned again for all NRT users according to the proportional fairness strategy so as to maximize the total rate of the system possibly.

3.1 Resource allocation for fixed rates of RT users

It needs to determine the attributive relations of user and subcarrier before the bits and power are allocated to subcarrier. In order to distinguish the service between different users, the scheduling priorities of all users must be firstly calculated, which involves many factors such as the largest allowable time delay of user, the required average rate and channel state, the fairness of use-selection and the diversity gain of multi-user. For each RT user, the fixed rate must be transmitted within the maximum time delay. The user closest to its deadline with the best channel state is selected for scheduling firstly, so the priority of subcarrier u assigned to RT user i is expressed as [20]

          (12)

where w_i is the waiting time of head packet of user i in its queue, η_i is the weight factor of user i having relations to the maximal time delay T_i, fixed average rate R_i1 and the completed average rate u_i, which can be expressed as

                            (13)

and in Eq.(12),  is the statistical average of η_iw_i of all RT users, which is written as

                          (14)

The allocation steps of the resource for the fixed rates of all RT users are as follows.

1) Suppose that the initial subcarrier set is U₁=   {1, 2, …, N} and u_i for each RT user i is 0.

2) Subcarrier n is assigned to RT user k according to the following equation:

                   (15)

The subcarrier n is removed from the set U₁. If the set U₁ is empty, the step of subcarrier allocation for RT users is finished. Otherwise, repeat this step until the set U₁ is empty.

3) The subcarrier set S_k is calculated for each RT user k, and the power is assigned in all set S_k by adopting the bit adding looking-up table method [14] to minimize the total power used with some restrictions until the assigned rates of all RT users are their fixed rates or the power of the system is used up or any restriction of the model is breached. Wherein, the RT user attaining its fixed rate will stop to be assigned any resource and its unused subcarriers will be assigned again to the RT user non-attaining its fixed rate according to Eq.(15).

4) The assigned rates are calculated for all RT users. If the fixed rates of RT users are all satisfied, the remainder total power of the system and unused total subcarriers are calculated. Otherwise, the algorithm is over.

3.2 Resource allocation for minimal rates of NRT users

Because the NRT users have no strict time delay demands, the remainder resource allocation of the system for NRT users should maximize the total throughput of the system possibly when the remainder resource is not sufficient for the minimal rates of all NRT users. Otherwise, the remainder resource allocation of the system for NRT users should minimize their total power used with satisfying the minimal rates of all NRT users. When the sub-carrier u is not assigned to RT user, its priority for assigning it to NRT user i is expressed as

                  (16)

ω_i is the weight factor for NRT user i, which is

                           (17)

where u_i is the completed average rate for NRT user i, and R_i2 is the minimal average rate for NRT user i.

The remainder resource allocation steps for the minimal rates of all NRT users are expressed as follows.

1) The remainder total power P_res and the unused subcarrier set U₂={1, 2, …} are calculated after the resource allocation of RT users. Let u_i for each NRT user i be 0.

2) Subcarrier n is assigned to NRT user k according to the following equation:

                 (18)

The subcarrier n is removed from the set U₂. If the set U₂ is empty, the step of subcarrier allocation for NRT users is finished. Otherwise, this step will be repeated until the set U₂ is empty.

3) The subcarrier set S_k is calculated for each NRT user k, and the power P_res in all set S_k is assigned by adopting the bit adding looking-up table method [14] to minimize their total power used. If the power P_res is satisfactory, the bit adding process will be repeated until the assigned rates of all NRT users are their minimal rates or any restriction of the model will be breached. Otherwise, the total assigning rate of NRT users will be maximized possibly under the remainder total power and the various restrictions of the system. Wherein, the NRT user attaining its minimal rate will stop to be assigned any resource and its unused subcarriers will be assigned again to the NRT user non-attaining its minimal rate according to Eq.(18).

4) The assigned rates are calculated for all NRT users. If the minimal rates of NRT users are all satisfied, the remainder total power of the system and unused total sub-carriers are calculated once again. Otherwise, the algorithm is over.

3.3 Remainder resource allocation for NRT users according to proportional fairness strategy

If the minimal rates of NRT users are all satisfied and the remainder power resource of the system and/or subcarrier is not used up, firstly the remainder subcarrier of the system is optimally assigned to NRT user, then based on the assigned resource of all NRT users, the remainder power of the system is also assigned to NRT user according to the proportional fairness strategy until the remainder resource is used up. When the subcarrier u is not assigned to any user, its priority for assigning it to NRT user i is expressed as

                  (19)

The remainder resource allocation steps of the system for NRT users according to the proportional fairness strategy are as follows.

1) The remainder total power P_res of the system and the unused subcarrier set U₃={1, 2, …} are calculated. If the set U₃ is not empty, the priority of every subcarrier u in the set U₃ is calculated according to Eq.(19) and the sub-carrier u is assigned to NRT user i according to Eq.(18).

2) The NRT user k is selected according to the following equation:

                         (20)

Then, the resource of 1 bit is assigned by adopting the bit adding looking-up table method based on the assigned resource of NRT user k and with the restrictions of sub- carrier set S_k, remainder total power P_res, maximal bits and power for each subcarrier in set S_k. Lastly, the correlative parameters of NRT user k are updated. This step will be repeated until the remainder total power of the system is used up or any restriction of the model will be breached.

3) The resource allocation results for every user on every subcarrier in the first OFDM symbol, and the total remainder power and unused subcarriers as well as the other system performance parameters are calculated.

3.4 Resource adjustment of latter OFDM symbol

Suppose that the resource allocation results of the former OFDM symbol in each frame are taken as the resource allocation of its successive OFDM symbol. Under the new channel state  and the preassigned power p_k,n for every used user-subcarrier pair (k, n), its preassigned bits are calculated according to the following equation:

            (21)

The above bits preassigned could make the assigned total rate R_k of any user k larger than its required value R_k,req, which is the fixed rate for RT user and is the minimal rate for NRT user, so the user set V={k|R_k,req<  R_k} could not be empty and the assigned redundant resource of any user k in set V could be released until the set V is empty. The power decrease Δp_i,u(r_i,u) for releasing 1 bit on the used user-subcarrier pair (i∈V, u∈S_i) could firstly be calculated according to the following equation:

                     (22)

where r_i,u is the assigned bits on the user-subcarrier pair (i, u). Then, the user-subcarrier pair (k, n) is selected according to the following equation:

                 (23)

Lastly, the assigned resource of 1 bit is released on the user-subcarrier pair (k, n).

Owing to the diversification of the channel state of two adjacent OFDM symbols, the subcarrier (m, n) in set S_k for user k in the former OFDM symbol does not satisfy the following equation, but the one in the latter OFDM symbol may meet the following equation as

 (24)

So, it is necessary to confirm the possible bit- swapping subcarrier pairs (m, n) for any user k according to Eq.(24) to estimate the conditions of bit-swapping and to do some bit-swapping and power-adjustment according to the following equation so as to satisfy the optimal allocation rule [11] and decrease the total power used possibly while maintaining the assigned total bits for user k:

(25)

where  is the maximal available bits on (k, n) as

             (26)

The adjustment flow chart of resource allocation for the successive OFDM symbol is described in Fig.1.

4 Simulation and analysis

The numerical results demonstrate the performance of proposed algorithm in the practical power-line channel scenarios [11]. Suppose that the available subcarrier number of each OFDM symbol is 128, the frequency range is 0-20 MHz and the channel encoding is not used. The transmitting signal PSD mask is -50-0.8f (dBm/Hz) and the total noise PSD for each user is -96+ 46.7exp(-1.6f) (dBm/Hz), where the unit of f is MHz. The maximal number of bits on each subcarrier is 8 and the total power of the system is 10 mW. RT user set Ω₁ is {1, 2} and its user number K₁ is 2 with the target BER of 10^-4. NRT user set Ω₂ is {3, 4} and its user number K₂ is 2 with the target BER of 10^-6. Suppose that the required rate of user 1 is the benchmark rate R₁ (bits per system), then the fixed rates of RT users are {R₁, 0.6R₁} and the minimal rates of NRT users are alterable. Let the maximal time delay of user 1 be one with the normal unit, then the maximal time delay of user 2 is δ, where δ is the relative delay factor. For the sake of simplicity, it is supposed that each frame only involves two OFDM symbols. Wherein, the resource allocation in the first OFDM symbol is normal, which is remarked as 01, and the allocation in the second OFDM symbol is adjustment, which is remarked as 02. For the comparison, when it is also assigned normally, it is remarked as 22.

Fig.1 Adjustment flow chart for successive resource of OFDM symbol

Fig.2 depicts the unit power SNR curves of all users in the two contiguous OFDM symbols of one frame. Wherein, the SNR of latter OFDM symbol for every user is added with a normal distribution stochastic variable with the average value of -2 and the standard deviation of 2 on the basic SNR of former OFDM symbol. The transformations of all curves are similar with the same subcarrier number, but the transformations of RT users are better than those of the NRT users by and large.

Fig.3 and Fig.4 show the resource allocation results of proposed algorithm under the benchmark rate R₁ of  40 bits/symbol, the relative delay factor of 1.25 and the minimal rates of NRT users of {0.8R₁, 0.4R₁}. From Fig.3, we can obtain that every subcarrier in every OFDM symbol is mostly used by one user and the assigned number of bits on it satisfies its restrictions. Some subcarriers are not assigned with any bit because they are poor to every user when the system resource is enough or even moderate to some users when the system resource is in shortage. There are many bits assigned on some subcarriers because of their good channel states to the relevant users. Certainly, some subcarriers, favorable to some users, are not always assigned with more bits because they have relation with the users of these subcarriers. From Fig.4, it can be observed that the assigned power on every subcarrier is below its relevant signal PSD mask value. The closed subcarriers must not be assigned with any power, and the assigned power on the used subcarriers is not always proportional to their assigned bits because the assigned resource has relations not only with the attributive users of these subcarriers, but also with their channel states. From Fig.3 and Fig.4, the allocation results of 01 and 22 modes are not the same because of the difference in the channel state of the two contiguous OFDM symbols in one frame. However, due to the small difference of channel state and the same allocation mode, constraints and requirements, their results of resource allocation are very similar. The allocation results of 02 mode are slightly different from those of the 22 mode because of the different allocation modes with the same channel states, constraints and requirements, so that their similar results of resource allocation demonstrate that the adjustment of resource allocation for the successive OFDM symbol in one frame is feasible.

Fig.2 Unit power SNRs of each user in two contiguous OFDM symbols: (a) Former; (b) Later

Fig.5 illustrates that the effect of related delay factor δ on the total assigned rate at the benchmark rate R₁ of 50 bits/symbol and the minimal rates of NRT users of {0.8R₁,0.4R₁}. It is shown that the effect of alterable value δ on the total assigned rate of every allocation mode is in some stages. With δ increasing, although the results of all modes increase in some time and decrease in some time, the total tendency of 01 mode increases, the results of 02 and 22 modes are almost the same as the large or little values of δ, and the changing range of result for 02 mode is larger than that of 22 mode but the whole result for 02 mode is less than that of 22 mode and they are all less than that of 01 mode. By comparing the results of 02 and 22 modes, the effect of δ changing on the resource allocation is variable because the total rate of resource allocation has relation with the assignment of subcarrier to user, which has relation with the value of δ. It is shown that the assigned total rate of 02 mode is larger than that of 22 mode with the range of δ from 0.6 to 0.75. This shows that the effect of δ changing from 0.6 to 0.75 on the assignment of subcarrier to user is in the major status. But, no matter how δ value varies, the total rate of 02 mode is very close to that of 22 mode statistically, that is, the performances of adjustment resource allocation for 02 mode are close to those of the normal allocation for 22 mode.

Fig.3 Assigned number of bits on every subcarrier: (a) 01 mode; (b) 02 mode; (c) 22 mode

Fig.4 Assigned power on every subcarrier: (a) 01 mode; (b) 02 mode; (c) 22 mode

Fig.5 Effect of relative delay factor on assigned total number of bits

Table 1 shows the effect of diverse user rates required on the results of resource allocation with the relative delay factor of 1.25 and the minimal rates of NRT users of {0.8R₁, 0.6R₁}. When the benchmark rate is less than 60 bits/symbol, the required rate of every user can be satisfied, that is, the allocated rate for RT user is fixed and the rate for NRT user is larger than its minimal rate. With increasing the benchmark rate, the rates of RT users are all satisfied, but the rates of NRT users decrease for 01 mode and increase then decrease for 02 and 22 modes, and the differences of allocated rate and relevant minimal rate are less. With increasing the benchmark rate, the remainder total power of 01 mode is always the largest and that of 02 and 22 modes increases in some time and decreases in some time, but their total tendency decreases and that of 22 mode is always less than that of the 01 mode. With the increase of benchmark rate, the total tendency of used time for all modes decreases little, while the total tendency of the 01 mode is firstly not larger than that of 02 mode and then not less than that of 02 mode, but the total tendency of 02 mode is firstly less than that of 22 mode and then larger than that of 22 mode. When the benchmark rate is large, the rates of some or all NRT users cannot be met while the rates of all RT users are still met, the remainder total power is not too large and the used time is relatively fixed at this time. By comparing the results of 02 mode and 22 mode, it can be found that their performances are very similar statistically but the used time of 02 mode is often less than or close to that of 22 mode. All of these illuminate that not only the adjustment mode of resource allocation is feasible but also its applied performances are superior to the normal allocation mode.

Table 2 lists the effect of diverse user rate required on the results of the used power for RT users and the assigned rate ratio for NRT users with the relative delay factor of 1.25 and the minimal rates of NRT users of {0.8R₁, 0.4R₁}, {0.8R₁, 0.6R₁}, {0.8R₁, 0.8R₁}, {0.6R₁, 0.8R₁} and {0.4R₁, 0.8R₁}. We can obtain that with the increase of benchmark rate, the used powers for RT users all increase, while the used power of 01 mode is always less than that of 02 mode because of the difference of channel state and the allocation mode, but the used power of 02 mode for RT user 1 is always not less than that of 22 mode and the used power of 02 mode for RT user 2 is always not larger than that of 22 mode. This also shows the advantage of 02 mode. With the increase of benchmark rate, the assigned rate ratios of NRT user 1 and NRT user 2 are all close to the required values when the minimal rates of NRT users are all satisfied. This is because the remainder resource of the system is assigned to all NRT users according to the proportional fairness strategy at this time. Otherwise, the assigned rate ratios of NRT user 1 and NRT user 2 are far away from the required values because of having no remainder resource allocation by the proportional fairness strategy.

Table 1 Comparison of resource allocation results in diverse required rates

Table 2 Comparison of used power of RT users and rate ratio of NRT users in diverse required rates (01 mode/02 mode/22 mode)

5 Conclusions

1) An adaptive bit and power allocation model for multi-user multi-service OFDM-based PLC systems is analyzed with many practical restrictions.

2) A novel resource dynamic allocation algorithm with the rate and power adaptation is proposed for the model above. In the first OFDM symbol of each frame, the resource of the system is firstly assigned for every RT user so as to satisfy the fixed rates and minimize the total used power; then the remainder resource of the system is assigned for every NRT user so as to satisfy its minimal rate and minimize the total used power; lastly the remainder resource of the system is assigned for every NRT user so as to maximize its total assigned rate. Bits are swapped and power is adjusted for every user in the latter OFDM symbol of each frame based on the resource allocation results of anterior OFDM symbol.

3) The proposed algorithm is tested in some typical power-line channel scenarios and the results indicate that it has better performances than the classical algorithms of multi-user resource allocation and it satisfies the multiple aims of multi-user multi-server resource allocation better.

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(Edited by YANG Bing)

Foundation item: Projects(51007021, 60402004) supported by the National Natural Science Foundation of China

Received date: 2009-08-31; Accepted date: 2010-06-07

Corresponding author: XU Zhi-qiang, PhD candidate; Tel: +86-10-81896912; E-mail: xu8282836@163.com